combination equation

Printable View

June 18th 2009, 12:21 PM
dhiab

combination equation

Solve in R : http://www.mathramz.com/xyz/latexren...607c586717.png
n , p naturels numbers and http://www.mathramz.com/xyz/latexren...161b4d985c.png
June 18th 2009, 01:21 PM
TheAbstractionist

Observe that

$^{n-1}\mathrm C_{p-1}\,+\,^{n-1}\mathrm C_p\ =\ ^n\mathrm C_p$

Hence

$x^2\,-\,^n\mathrm C_px\,+\,^{n-1}\mathrm C_{p-1}\cdot^{n-1}\mathrm C_p$

$=\ x^2\,-\,\left(^{n-1}\mathrm C_{p-1}\,+\,^{n-1}\mathrm C_p\right)x\,+\,^{n-1}\mathrm C_{p-1}\cdot^{n-1}\mathrm C_p$

$=\ \left(x\,-\,^{n-1}\mathrm C_{p-1}\right)\left(x\,-\,^{n-1}\mathrm C_p\right)$
June 18th 2009, 10:30 PM
dhiab

Quote:

Originally Posted by TheAbstractionist

Observe that

$^{n-1}\mathrm C_{p-1}\,+\,^{n-1}\mathrm C_p\ =\ ^n\mathrm C_p$
Hence

$x^2\,-\,^n\mathrm C_px\,+\,^{n-1}\mathrm C_{p-1}\cdot^{n-1}\mathrm C_p$
$=\ x^2\,-\,\left(^{n-1}\mathrm C_{p-1}\,+\,^{n-1}\mathrm C_p\right)x\,+\,^{n-1}\mathrm C_{p-1}\cdot^{n-1}\mathrm C_p$

$=\ \left(x\,-\,^{n-1}\mathrm C_{p-1}\right)\left(x\,-\,^{n-1}\mathrm C_p\right)$

Hello : Thank you
it is necessary to discuss the number of resolution according to paramétres n , p (Itwasntme)

All times are GMT -8. The time now is 05:44 AM.

Copyright © 2005-2013 Math Help Forum. All rights reserved.

Copyright © 2005-2013 Math Help Forum. All rights reserved.